Category: General / Topics: Statistics

Those Pesky Zeros, Part 2

The other side of the decimal point

by Stu Johnson

Posted: June 23, 2015

Part 1 looked at large numbers, now we cross over to the right side of the decimal point and look at some examples from sports where time is measured in fractions of a second…

While large numbers can become mind-numbing—the focus of Part 1 of this blog—I have also been fascinated by the impact of technology on sports, where accuracy keeps moving the number of zeros on the other side of the decimal point.  It’s a situation of opposites, as illustrated by the two charts above.

On the left is the exponential growth of GDP over the history of the American republic.  The point of the previous blog was the need to maintain a sense of significance as the universe of numbers we’re looking at gets larger and for practical reasons we move the decimal point a thousand-fold, from millions, to billions, to trillions—leaving “mountains within mountains.” 

The world of sports is just the opposite, as illustrated in the century-long history of marathon records on the right.  In this case, the record dropped significantly at first and then the rate slowed down to smaller and smaller increments as the limit of human performance approached. In a number of sports, the early achievements came fairly easily with improved techniques and factors like clothing (particularly noted in swimming) or footwear (track & field).

More recently, as we close in on the seeming limits of human capability, high-tech motion analysis, super-slow-motion video, materials science and other research have helped eke out ever-smaller improvements in time. Because breaking the record or winning in competition is still the goal, the results are often measured in increments so small that they appear as a tie to the real-time observer. We’ll look at some famous examples from the Olympics later.

In my lifetime, I can remember watching Wide World of Sports on ABC or Olympics coverage when stop watches were still used in some events. With the advent of electronic timing, the accuracy quickly went from tenths to hundreds of a second. While capable of going down even further, it seems that hundredths is the current standard for most timed events. The IAAF (International Amateur Athletics Association) required timing to hundredths of a second in 1977.

A friend recently said he had been to a Pinewood Derby® event where the timers read out in thousandths of a second. Imagine doing everything possible to get every bit of speed out of your little racer, then losing out by a thousandth of a second!  Taking a quick look at Pinewood Derby® links, it did appear that most digital timers do read out to the thousandth of a second, though one (Smartline) claimed  that it “supports up to 8 lanes with instant race results resolved to .00005 seconds.” [1]  Of course, there is a matter of scale when you’re racing a tiny car on a 35-40 foot track, instead of a full size car going multiple laps on a quarter-mile to two-mile track.  

Several years ago, while visiting my brother in Ann Arbor, Michigan we went with his family as they participated in the annual “Turkey Trot.”   A typical 5K event, a relative handful of participants are attentive to their time, while the majority seemed to show up to trot or walk while wearing Thanksgiving-themed headwear or clothing—not so much a competitive sports event as a communal holiday celebration of late-fall before the approach of winter. That year the race was timed, with each runner given a tag with an RFID chip to record their precise time as they passed the start/finish line.

I discovered that this technology was introduced in 1993, with a shoe-mounted timing chip by Netherlands-based ChampionChip.  Little changed until 2007 when a disposable chip introduced by Innovative Timing Systems made this technology much less expensive to deploy. Originally designed for tracking inventory by retailers like Wal-Mart and Target, these chips were cheap, disposable, and waterproof. They could be adhered to racing bibs or stick-on strips for shoes. [2]

Despite the relative ease of the technology, by the time we returned to the Turkey Trot last year, they had moved the race from the north campus of the University of Michigan to downtown Ann Arbor, and dropped the timing.  Community, in this case, was more powerful than competition.

Back to competition...what happens when races end in what appears to be a tie?


The concept of photo-finishes began with horse racing.  In fact, an early concept of “motion picture” is attributed to Eadweard Muybridge, who in 1878 used multiple cameras along a track in Palo Alto, California to help answer the question of whether a running horse had all four hooves off the ground at the same time (it did). [5]   More than a century ago, Muybridge anticipated much of what we see today in many sports. In a letter to the editor written to Nature in May of 1882, he stated “I venture to predict, in the near future that no race of any importance will be undertaken without the assistance of photography to determine the winner of what might otherwise be a so-called ‘dead-heat’.” [6]

That quote comes from a fascinating article in Scientific American about the development of the photo finish in horse racing. It required much more than snapping a shot of the finish line with a camera. Careful attention to lighting, camera placement, aperture setting, and other factors were necessary to get a precise, crystal-clear picture across the track in order to definitively judge a winner.  Today, high speed video cameras can provide similar images with the same hundredths-of-a-second accuracy (or better) as standard timing devices.

Breaking ties

There are many examples in horse racing, auto racing, and other sports. Here are three examples from the Olympics.

Women's 100-meter dash trail 2012

In the 2012 Olympic Trials, the women’s 100-meter dash resulted in a dead heat for third place between Allyson Felix and Jenebah Tarmoh.  The timer had initially ruled Tarmoh the winner by one thousandth (not one hundredth) of a second, but the photo (above) revealed an absolute tie (in track events the determination is based on the position of the torso). There was no protocol in place, as there was in other sports—typically with a runoff. The USTAF announced the option of a coin-toss or a runoff. If both racers agreed, the chosen option would be used. If they disagreed, the tiebreaker would be a runoff. If both declined, it would be a coin toss.  Before the issue could be settled, however, Tarmoh withdrew and Felix had the spot for the 100m. Tarmoh came in fifth in the 200m, meaning that doing the runoff could have been her chance for an individual spot on the team. She was, however, part of the 4x100m relay pool. [3]

From, here are two of “10 Insanely Close Olympic Finishes.” [4]

Phelps and Cavic 100-meter butterfly 2008

100-Meter Butterfly, 2008.  The 100-meter butterfly was the only race Michael Phelps swam at the 2008 Olympics for which he did not already hold the world record. American-born Milorad Cavic, competing for Serbia, set an Olympic record in the first round and led the field halfway through the final, with Phelps trailing in seventh place. In a sensational finish, Phelps surged over the final 50 meters, making up a deficit of more than half a second to touch in a virtual tie with Cavic that was too close to call by the naked eye. The results of swimming races are now determined not by a photo, but by the pressure applied to touch pads. Omega, the official timekeeper of the Olympics (and one of Phelps’ sponsors) announced that Phelps had won by 4.7 millimeters (one-sixth of an inch).
Photo: Mark J. Terrill/AP

In a case like this, where the results are virtually a tie, I wonder if the timing system itself is so accurate (in this case an underwater touch pad) to be absolutely trustworthy. Is there any margin of error or are the devices 100.000% accurate all the time? 

1992 Olympics Women's 100-meter dash

The 100-meter final in Barcelona, 1992, was the closest track race in Olympic history. Gail Devers (Lane 2) of the United States and Irina Privalova of Russia (Lane 6) ran almost even most of the race, but Jamaicans Julie Cuthbert (Lane 3) and Merlene Ottey and American Gwen Torrence all came on at the end. It was impossible to tell who had won until slow-motion replays of the finish were shown in the stadium. Even then, one couldn’t be sure. The official announcement finally gave the victory to Devers. Ottey ended up in fifth place, even though she was less than one-tenth of a second behind the winner.
Photo: Manny Millan/Sports Illustrated/Getty Images

Imagine – coming in one-tenth of a second under the leader and still being number 5!  Or, as has occurred in a number of basketball games—where the clock ticks off tenths of a second—losing a game as your opponent sinks a shot literally “at the buzzer.” 

The ultimate question

After all of this is said and we see the ability of technology to determine the breaking of records or settling ties by infinitesimal amounts, the question arises, “how far should this go?”  I am admittedly not a sports-junkie, so I know some will argue my point as the price of competition. In fact, I resist the tendency in modern culture to downplay competition and to lower the bar to avoid hurt feelings—I strongly believe in striving for and honoring excellence. However, just as I argued in Part 1 not to lose sight of significance inside very large numbers—moving the decimal point—I would also argue that we can assign too much significance as we move to the right of the decimal point, declaring winners by the tip of a fingernail, the thickness of a running jersey, or the tiniest fraction of a second.


  1. For general information on Pinewood Derby®, I found quite a few links on
  2. The Evolution of Race Timing Technology -
  3.  From The Week - and SBNation -
  4. From -
  5. “The Man Who Stopped Time” in the Stanford University alumni magazine -
  6. See Scientific American -

Stu Johnson is owner of Stuart Johnson & Associates, a communications consultancy in Wheaton, Illinois focused on "making information make sense."

E-mail the author (moc.setaicossajs@uts*)

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Posted: June 23, 2015   Accessed 797 times

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